The problem here is word use. When you burn wood it does not become coal or charcoal. It turns into embers.

Embers are not coal and coal is not charcoal.

Technically to make wood into coal you need to slowly cook it without the presence of oxygen. If you just light it on fire wood becomes embers. Embers are perfectly fine for smoking hookah but have a very short life. They are not very dense and burn away quickly ashing a lot.